A treatise on infinitesimal calculus, Volumen 2 |
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Otras ediciones - Ver todo
A Treatise on Infinitesimal Calculus: Containing Differential and Integral ... Bartholomew Price No hay ninguna vista previa disponible - 2015 |
Términos y frases comunes
a₁ arbitrary constants axis b₁ becomes c₁ Calculus calculus of variations contained curvature cx² cycloid d.dx d²x d²y d²z definite integral derived-functions determined differential calculus differential equation double integral ds ds ds dx dx a² dx ds dx dx dx dy dz dx Ex dx₁ dx² dy dx dy dy dy² dz² element-function ellipse ellipsoid equa equal exact differential expressed formulæ geodesic lines geometrical Hence infinitesimal infinitesimal element involves length limits of integration lines of curvature maxima and minima plane curve polar coordinates problem radius Similarly substituting suppose surface symbol tangent Theorem tion values variables variation volume whence x2 dx y-integration αμ αξ λ² µ² ΦΩ
Pasajes populares
Página 294 - F3 are proportional to the directioncosines of the normal to the surface at the point (x...
Página 166 - ... is equal to the product of the length of the curve and the length of the path described by the centroid of the curve.
Página 213 - Let p be the length of the perpendicular from the centre of the atom to the original direction of motion BZ of the particle.
Página 286 - ... of any form and size. When stretched the rod becomes thinner, so that the several particles undergo lateral as well as longitudinal displacements. There is one fibre or line of particles which is undisturbed by the lateral contraction. Let this straight line, which we may regard as the central line, be taken as the axis of x, and let the origin be at the fixed extremity of the rod. We suppose that the stretching forces at the two ends are distributed over the extreme cross sections in such a...
Página 337 - F' (x) is the trigonometrical tangent of the angle between the axis of x and the tangent to the curve at the point (x, y). Art. 38. Let OM=x1, MN=h, Ffa+k)-Ffa) h then is the tangent of the inclination of the chord PQ to the axis of x. Hence Art. 101 amounts to asserting that at some point R between P and Q the tangent RT to the curve is parallel to PQ. We call this an illustration. When, however, the student has sufficiently...
Página 502 - Find the curves in which the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact. [The circles r - 2a cos в.] 13.
Página 510 - By making *' = 0, we find the co-ordinates of the point where the normal meets the plane of xy, also, the length of the normal, intercepted between the surface and the plane of wy, is РнoB.
Página 170 - ... and one of whose edges passes through the centre of the sphere. Find the area of the surface of the sphere intercepted by the cylinder. .Let the cylinder be perpendicular to the plane of xy ; then the equations of the cylinder and the sphere are respectively yz = ax — x2 and я2 -f y2 + z2 = a*.
Página 348 - R ' ( } where P, Q, and R are functions of x, y, and z.
Página 502 - A. + u for the rectification of a plane curve, where p is the perpendicular from any assumed point called the pole on a tangent to the curve, A the angle between this perpendicular and any fixed line drawn through the pole, u the portion of the tangent intercepted between the point of contact and the foot of this perpendicular. Let Q be the centre of curvature of the arc at A, AB a tangent at A...